Legend:

Below is a summary of the above listed in order of what I think is decreasing controversy.

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1. A=sage.combinat.partition.number_of_partitions() is marked for deprecation in favour of B=sage.combinat.partitions.number_of_partitions(), which is what function A() calls most of the time. As agreed above, number_of_partitions() will stay in the global name space, but this made the deprecation somewhat fiddly as I did not want to deprecate number_of_partitions() for "normal use" because from the user perspective this function will not change. Instead, I have deprecated the individual options of number_of_partitions() so deprecation warnings are only generated when A() does NOT call B(). In the global namespace, number_of_partitions still points to A(). When the functions which are marked for deprecation below are removed, number_of_partitions() should be changed to point to B() and A() should be changed into a deprecated_function_alias to B(). See the patch for more details.

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2. For use in Partitions().random_element() the function number_of_partitions() was cached. This cached function was almost never used so, assuming that caching this function is a good idea, I decided to cache sage.combinat.partitions.number_of_partitions() always. Please let me know if this is a bad idea.

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3. The two functions

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* cyclic_permutations_of_partition

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* cyclic_permutations_of_partition_iterator

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are deprecated in sage.combinat.partition and they have been moved to sage.combinat.set_partition and renamed ...._of_set_partition... As far as I can tell these functions are never used but, in any case, they are methods on set partitions rather than partitions. Nonetheless, they need to be deprecated from the global name space.

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4. The following functions were marked for deprecation several years ago so they have been removed from sage.combinat.partition.py:

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* RestrictedPartitions

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* partitions_list

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* number_of_partitions_list

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* partitions_restricted

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* number_of_partitions_restricted

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5. The following functions now give deprecation warnings and are marked for removal from the global name space:

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* partitions_set

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* number_of_partitions_set

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* ordered_partitions

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* number_of_ordered_partitions

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* partitions,

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* ferrers_diagram

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* partitions_greatest

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* partitions_greatest_eq

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* partitions_tuples

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* number_of_partitions_tuples

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* partition_power

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In all cases, these function are deprecated in favour of (methods in) parent classes.